How do I find the line representing the intersection of two planes?

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Felipe Dicker 2021-4-9

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评论： Hussain Bukhari 2022-11-10

So basically I have two planes and need to find the equation of the straight line which is the intersection between the two. I'm having trouble finding the equation of said planes and then equaling them to each other to find the equation of the straight line. I do know the coordinates of three points on each one of the planes. Any help? Here are the points:

% Plane 1
A = [1 1 1];
B = [2 -3 5];
C = [-7 2 1];
% Plane 2
D = [0 5 3];
E = [8 -4 2];
F = [5 4 1];

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Matt J 2021-4-9

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编辑：Matt J 2021-4-9

在 MATLAB Online 中打开

HINT: You can get the normals to the planes using cross()

% Plane 1
A = [1 1 1];
B = [2 -3 5];
C = [-7 2 1];
% Plane 2
D = [0 5 3];
E = [8 -4 2];
F = [5 4 1];
normal1=cross(B-A,C-A)
normal1 = 1×3
    -4   -32   -31
normal2=cross(E-D,F-D)
normal2 = 1×3
    17    11    37

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John D'Errico 2022-11-10

@Hussain Bukhari - this is clearly a homework problem. And we try not to do homework assignments for students on Answers. Doing that does not help the student, beyond giving them an undeservedly good grade on their current homework. So @Matt J pointed the student in the right direction, but then stopped.

Hussain Bukhari 2022-11-10